let GF be non empty right_complementable associative well-unital distributive Abelian add-associative right_zeroed doubleLoopStr ; :: thesis: for V being non empty right_complementable VectSp-like Abelian add-associative right_zeroed VectSpStr of GF
for l being Linear_Combination of {} the carrier of V holds l = ZeroLC V
let V be non empty right_complementable VectSp-like Abelian add-associative right_zeroed VectSpStr of GF; :: thesis: for l being Linear_Combination of {} the carrier of V holds l = ZeroLC V
let l be Linear_Combination of {} the carrier of V; :: thesis: l = ZeroLC V
Carrier l c= {} by Def7;
then Carrier l = {} ;
hence l = ZeroLC V by Def6; :: thesis: verum